For our consideration of a constant metric, the term in brackets from the
above equation can be recognized as the proper length \(L_{p}\)  [1]},
\(L_{p}=\int _{0}^{L}\sqrt{-\frac{1}{g^{\xi \xi }}}~d\xi =L\sqrt{-\frac{1}{g^{\xi \xi }}}~. \) 
